Step By Step Calculus » 10.0 - History and Applications

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History and Applications

Although Newton (1643 -1727) and Leibniz (1646 -1716) are considered to be the main contributors to the modern calculus, the concept of a derivative in the sense of a tangent line is a very old one, familiar to Greek mathematicians such as Euclid (c. 300 BC) and Archimedes (c. 287 BC -212 BC).

We have seen the definition of derivative as a rate of change and also interpreted it as the slope of a function. It would be tedious if we always had to use the definition, so in this chapter we develop derivative rules that can be applied directly. One can then use these rules to solve problems involving rates of change that arise from a variety of applications. For example, an engineer wants to know the rate at which water is pumped out from a resorvoir, an economist wants to know marginal cost (the rate at which cost increases with the increase of production), a meteorologist wants to know the rate of increase in wind velocity with respect to height, an environmentalist wants to know the rate at which the earth is warming up, a business analyst wants to know the rate at which the demand of a particular product is changing. Actually, you will find application involving rates of change in almost every area of science, engineering and business.